On the stable decomposition of Ω²𝑆^{𝑟+2}

Brown, E. H.; Peterson, F. P.

doi:10.1090/S0002-9947-1978-0500933-4

On the stable decomposition of $\Omega ^{2}S^{r+2}$
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by E. H. Brown and F. P. Peterson

Trans. Amer. Math. Soc. 243 (1978), 287-298

DOI: https://doi.org/10.1090/S0002-9947-1978-0500933-4

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Abstract:

In this paper we show that ${\Omega ^2}{S^{r + 2}}$ is stably homotopy equivalent to a wedge of suspensions of other spaces $C_k^1$, and that $C_k^1$ is homotopy 2-equivalent to the Brown-Gitler spectrum.

References

V. I. Arnol′d, Topological invariants of algebraic functions. II, Funkcional. Anal. i Priložen. 4 (1970), no. 2, 1–9 (Russian). MR 0276244
Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
Edgar H. Brown Jr. and Samuel Gitler, A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra, Topology 12 (1973), 283–295. MR 391071, DOI 10.1016/0040-9383(73)90014-1
Edgar H. Brown Jr. and Franklin P. Peterson, Relations among characteristic classes. I, Topology 3 (1964), no. suppl, suppl. 1, 39–52. MR 163326, DOI 10.1016/0040-9383(64)90004-7
Frederick R. Cohen, Thomas J. Lada, and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin-New York, 1976. MR 0436146, DOI 10.1007/BFb0080464
F. R. Cohen, M. E. Mahowald, and R. J. Milgram, The stable decomposition for the double loop space of a sphere, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 225–228. MR 520543

On odd primary homotopy theory

Edward Fadell and Lee Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111–118. MR 141126, DOI 10.7146/math.scand.a-10517
R. Fox and L. Neuwirth, The braid groups, Math. Scand. 10 (1962), 119–126. MR 150755, DOI 10.7146/math.scand.a-10518

Cohomologies of the group COS

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Mark Mahowald, A new infinite family in ${}_{2}\pi _{*}{}^s$, Topology 16 (1977), no. 3, 249–256. MR 445498, DOI 10.1016/0040-9383(77)90005-2
V. P. Snaith, A stable decomposition of $\Omega ^{n}S^{n}X$, J. London Math. Soc. (2) 7 (1974), 577–583. MR 339155, DOI 10.1112/jlms/s2-7.4.577